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%I #22 Feb 09 2018 09:12:51
%S 0,1,2,1,2,2,3,1,2,2,3,2,3,3,2,1,2,2,3,2,3,3,2,2,2,3,2,3,2,2,3,1,3,2,
%T 3,2,3,3,3,2,3,3,2,3,2,2,3,2,3,2,2,3,2,2,3,3,3,2,3,2,3,3,3,1,3,3,3,2,
%U 2,3,2,2,3,3,2,3,3,3,3,2,2,3,2,3,2,2,2,3,2,2,3,2,3,3,3,2
%N Number of steps to reach 1, starting with n and applying the A072084-map repeatedly.
%H Reinhard Zumkeller, <a href="/A072086/b072086.txt">Table of n, a(n) for n = 1..10000</a>
%e n=21: '11'*'111' -> '10'*'11' -> '11'*'1' -> '1'; i.e., 21=3*7 -> 6=2*3 -> 2*1 -> 1*1=1, therefore a(21)=3.
%p A072086 := proc(n) local c,i,j; c :=0; i := n;
%p while i > 1 do i:=A072084(i); c:=c+1 od; c end:
%p # Note that this gives A072086(0)=0 if desired
%p # without any additional case discrimination.
%p # _Peter Luschny_, Jan 16 2010
%t b[1] = 1; b[n_] := Times @@ Power @@@ (FactorInteger[n] /. {p_Integer, e_} :> {DigitCount[p, 2, 1], e}); a[n_] := Length[FixedPointList[b, n]] - 2; Array[a, 100] (* _Jean-François Alcover_, Feb 09 2018 *)
%o (Haskell)
%o a072086 n = fst $
%o until ((== 1) . snd) (\(i, x) -> (i + 1, a072084 x)) (0, n)
%o -- _Reinhard Zumkeller_, Feb 10 2013
%Y Cf. A072085.
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Jun 14 2002
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